Example#5 [1]}: Compute \(p\)  and \(\mathbf {u}\)  such that
\( \begin{split}&k\mathbf {u}+\nabla p=f\text{ in } \Omega \\&-\mbox{div}(\mathbf {u})=g\text{ in } \Omega \\&-p=p_0\text{ in }\Gamma .\end{split}\) 
